The present invention is generally related to the generation of a binary digital signal representing the square of an analog input signal. More particularly, the present invention takes advantage of the strictly binary nature of the output from an oversampled analog to digital converter to readily implement, in digital circuit form, a recursively specified digital circuit equation which generates the desired digital representation of the square of an analog input function.
In the construction of certain circuit breakers, a root mean square digital signal is required to be generated. In particular, it is desired to generate a representation for an I.sup.2 signal, where I represents current level. To design an RMS (root mean square) electronic circuit breaker, it is necessary to generate the value of I.sup.2 in digital form. This could be done by multiplying the digitized value of I by itself. Unfortunately, digital multipliers are expensive in terms of integrated circuit chip area. Furthermore, for a multi-channel circuit breaker, the problem is compounded. One could solve the multi-channel problem by sharing a multiplier resource with the different channels. However, this in itself requires complicated control circuitry. Accordingly, it is desirable to be able to implement the squaring function digitally without the use of a multiplier and control circuitry to time share the multiplier resource.
While the present invention has arisen out of the desire to compute the I.sup.2 function for use in electronic circuit breakers, it is, however, seen that the present invention is not limited thereto, but is applicable to any situation in which the squared function is desired and in which an oversampled analog to digital signal is present.
For a proper understanding of the present invention, it is necessary to appreciate the operation of oversampled analog to digital converter circuits. These circuits operate in a fashion to produce a string of binary signals representing zero and one values and whose summation is indicative of the (average) level of an analog input signal (usually over a short time period). Oversampled analog to digital conversion circuits typically operate at sampling frequencies which are much greater than the Nyquist frequency associated with the input signal which is being converted. The ratio of this sampling frequency to the Nyquist frequency is typically between about 10 and 1,000. This ratio assures that significant changes in the analog input signal do not occur over a large plurality of sampling times thus rendering "averages" more representative of instantaneous signals. Such conversion circuits are particularly useful and desirable in power line circuits or in any other circuits which exhibit high noise levels, particularly when noise is present in the form of spikes. Oversampled analog to digital conversion is typically carried out through the use of circuits known as delta-sigma converters. In many applications of these converters, the output circuit typically comprises a digital filter which often simply is a counter which accumulates a tally of the number of one-bits that exist in the output signal over a period of time. Periodically the counter is reset to zero and the generation of the next binary output signal is begun. The present invention takes advantage of the nature of the output signal from such oversampled analog to digital converters to not only generate the usual output signal y, but also the signal y.sup.2.